@Office_Shredder : Depends on the value of a :
if it is in (-1,1) then the terms become smaller,
if if is in {-1,1} then they also become smaller,
else they become larger, as n increases.

On the secound one, I know some Taylor expansions as I searched for them on wikipedia, and I know the [tex] e^{x} [/tex] expansion, as I have to get e^2x I think I will multiply that expansion by itself...